confused about "unwrap" vs "modifier unwrap"
You may be confusing the name of the modifiers, there is no &quot;UV Unwrap&quot; Modifier, there's only a UV Warp and a UV Project modifier.
Unwrapping, as you already know, is used to provide texture coordinates to an object so Blender knows how to apply a certain texture to the mesh geometry.
It is a manual process and sort of &quot;destructive&quot;, in the sense that if you change the object's geometry after unwrapping (through modeling, sculpting or creating new geometry) you may need to adjust your UVMap afterwards or totally unwrap any newly created geometry.
It is however the only way to obtain correct texture coordinates for complex shapes. It is also the only type of texture coordinates that can be exported from Blender. If you plan on using the model elsewhere (like a game engine, third party application, or external software) it is required to unwrap your model so image textures can be applied reliably in the destination application.
Apart from that you have &quot;generated&quot; type of texture coordinates like Object or generated, which can't be exported and are generated by the render engine (Cycles or EEVEE) at render time. For many common cases and workflows where manually unwrapping is undesirable or unpractival these will suffice, if you don't require exporting your models.
For certain corner cases or specific applications you can use the mentioned modifiers for certain tasks in parallel with unwrapping or in its place, but they are not universal replacements for unwrapping.
UV Warp Modifier
The UV Warp Modifier, added to an already unwrapped object, uses two other objects to modify or manipulate an already existing set of UV coordinates. It may be used when you want an animated texture, want the UVs to somehow react to other objects, or edit UV Maps directly from the 3D view with interactive visual feedback.

UV Project Modifier
The UV Project Modifier is used as a replacement for UV unwrapping to generate a UV map as if a certain image was being projected over the mesh from a certain point in 3D space, like a true slide projector. It is often used for video mapping and inserting 3D objects into a real filmed scene.